Question

Consider two firms, X and Y, that have identical assets and generate identical cash flows. X is an all-equity firm, with 1 million shares outstanding that trade for a price of $24 per share. Y has 2 million shares outstanding and $12 million dollars in debt at an interest rate of 5%. According to MM proposition 1, share price of y is $6.

a) If the annual earnings before interest and taxes for each firm are $5 million, what would be the cost of capital of X and of Y?

Answer 1

Solution:

As per MM Theorem, the capital structure of the company does not affect the Value of the firm.

The Value of the levered and the unlevered firm is same. MM Proposition I does not consider the impact of corporate taxes.

In case of our example Company X and Y have identical assets and identical cashflows. Hence they will have same value.

Lets calcualte value of each company.

Company X      
No of shares   1   million
Price per share   24  
Value of the Equity : 24   Million
Debt   0  
Value of the company X = 24 + 0 =   24   Million

Company Y     
No of shares   2   million
Price per share   6  
Value of the Equity   12   Million
Debt   12  
Value of the company Y = 12 + 12 = 24   Million

Both have same value.

Also the WACC of both the companies will be same.

WACC of Company X = Cost of equity = 5/24 = 20.83%

WACC of COmpany Y = WACC of COmpany X = 20.83%

We may want to know what is the breakup of WACC of Company Y

Cost of Debt = 5%

Cost of Equity (as calculated by MM I - Proposition II) = 20.83% + (D/E) *(20.83% - 5%) = 20.83% + (12/12) *(20.83% - 5%) = 36.67%

So cost of equity increases as leverage increases, so thet WACC remains constant and hence the value of the firm.

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